hw41 - 3 = 7 x 2 + x 3 = 9 (b) Write this system in matrix...

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ECE360 HOMEWORK #4 DUE: FRIDAY, OCTOBER 5, 2007 Problem 4.1 Consider the following matrices: A = 1 1 0 1 0 1 0 1 1 , A 1 = 4 1 0 7 0 1 9 1 1 , A 2 = 1 4 0 1 7 1 0 9 1 , A 3 = 1 1 4 1 0 7 0 1 9 (a) Compute det( A ), det( A 1 ), det( A 2 ), and det( A 3 ) using Sarrus’ rule for determinants. (b) Compute det( A ), det( A 1 ), det( A 2 ), and det( A 3 ) using Chio’s pivotal condensation method. (c) Find A T and A - 1 = adj( A ) det( A ) Problem 4.2 Refer to Problem 4.1. (a) Check by direct substitution that x 1 = 1, x 2 = 3, and x 3 = 6 are solutions of the following system of equations: x 1 + x 2 = 4 x 1 + x
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Unformatted text preview: 3 = 7 x 2 + x 3 = 9 (b) Write this system in matrix form A x = b and solve for x = A-1 b . (c) Solve for x 1 , x 2 , and x 3 using Cramer’s rule, that is, evaluate: x 1 = det( A 1 ) det( A ) , x 2 = det( A 2 ) det( A ) , x 3 = det( A 3 ) det( A ) Problem 4.3 Find e At = L-1 ' ( sI-A )-1 “ given A = "-1 1-1 # Problem 4.4 Refer to Problem 4.3. Find: (a) A-1 (b) de At dt , Ae At , e At A (Conclude.) (c) Z t e Aτ dτ, A-1 ‡ e At-I · , ‡ e At-I · A-1 (Conclude.)...
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This document was uploaded on 11/01/2011 for the course ECE 360 at Boise State.

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